Question

Numerical type
The number of values of k for which the equation x^2 - 3x + k = 0 has two distinct roots lying
in the interval (0, 1) is​

Answer 1

Answer:

x²- 3x+k=0.

D=3

2 −4k=9−4k. For distinct real roots, 9−4k≥0 or k≤49

or k≤2.25 ...(i)

Now the roots of the above equation is given by

x

1= 23+ 9−4k

and x 2 =23− 9−4k

Now

0≤x

1 ≤1

0≤ 23+ 9−4k≤1

0≤3+ 9−4k ≤2−3≤ 9−4k ≤−1 ....(ii)

0≤x 2 ≤1

0≤ 23− 9−4k ≤1

0≤3− 9−4k ≤2−3≤− 9−4k ≤−1

3≥ 9−4k ≥1 ....(iii)

From (ii) and (iii),

9≥9−4k≥1

0≥−4k≥−8

0≤k≤2

Also, from (i),k≤2.25

Hence

k∈[0,2].

Now there are infinite real numbers between [0,2], hence there are infinite possible value of k.